Extreme weather events, such as thunderstorms, hails, hurricanes, and tornadoes, cause a significant amount of damage every year worldwide. In the United States, it is reported by the National Climate Data Center (NCDC)1 that there are eleven extreme weather events with at least a billion dollars' loss in 2012, causing a total of 377 deaths, which is the second most disastrous year in the recorded history. That said, much of the loss was due to a lack of proper precautions and could be avoided with a reliable severe weather warning system. 1 http://www.ncdc.noaa.gov/billions
Though meteorologists dedicate to making accurate weather forecasts with advanced computational technologies, the long-term prediction of severe storms is still not sufficiently accurate or reliable. In weather forecasting, computers are commonly applied to solve numerical models about weather systems, which are in essence partial differential equations (PDEs) that calculate the future conditions of a weather system from an initial condition. Due to the nonlinear and chaotic nature of numerical models, some tiny noises in the initial values can result in large differences in the predictions. This is commonly known as the butterfly effect. As a result, although nowadays powerful computers are used to run complex numerical models, it is difficult to get accurate predictions, especially in mid-to-long-term forecasting.
The numerical methods can efficiently process large amounts of meteorological measurements. However a major drawback of such methods is that they do not interpret the data from a global point of view at a high cognitive level. For instance, meteorologists can make good judgments of the future weather conditions by looking at the general cloud layout and developing trend from a sequence of satellite cloud images using domain knowledge and experience. Numerical methods do not capture such high-level clues. Additionally, historical weather records provide valuable references for making weather forecasts, but numerical methods do not make good use of them.